Boston’s leading arts and cultural institutions elevate spirits, but they lack appreciation for the high cost of providing police, fire, and road services to their patrons and employees. The city’s tax-exempt colleges and hospitals, for the most part, take a more enlightened approach when it comes to making voluntary payments in lieu of taxes, or PILOTs, to offset the costs of city services.

A new report from the nonprofit Boston Municipal Research Bureau shows that the 48 largest, private tax-exempt institutions in the city — ranging from Massachusetts General Hospital to Boston College High School — contributed nearly $20 million to the the city’s coffers in so-called PILOT payments in 2012. Hospitals and colleges complied admirably with the city’s requests, 96 percent and 88 percent respectively. The cultural institutions posted a pathetic 39 percent compliance rate.

In the past, these payments in lieu of taxes carried the whiff of a shakedown: Institutions paid up when they came in search of building permits and zoning variances. Now a sensible formula is in place that asks nonprofit groups with properties worth $15 million or more to pay 25 percent of what a for-profit owner would pay. That corresponds with the quarter of the city budget spent on services that directly benefit the institutions, such as public safety and snow removal.

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Nonprofit institutions are an irreplaceable source of jobs, prestige, and spending on local goods and services. But the ability to attract students, patients, tourists, and a talented workforce depends on Boston’s reputation as a safe and livable city. The “eds and meds’’ get the concept of mutualism and recognize the difficulty of running a city where half the land area is tax-exempt. Cultural institutions either don’t get it or prefer to view the city from sublime heights.

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The Children’s Museum, Institute of Contemporary Art, Museum of Science, and New England Aquarium made no cash payments last year. The Museum of Fine Arts, with property valued at $282 million, contributed just $56,000 — about a fifth of the amount requested. Only the Boston Symphony and WGBH paid their fair share.

MFA director Malcolm Rogers has been an outspoken critic of PILOT payments, even warning in an arts journal that putting the squeeze on cultural institutions would have “dire implications nationwide.’’ That’s a bit grandiose. A better definition of dire might be the failure of police or paramedics to respond to an emergency in one of the museum’s exhibit halls or restaurants.

New England Aquarium president Bud Ris makes a decent case that cultural institutions deserve gentler treatment from City Hall. Unlike universities or hospitals where first responders could be summoned at any hour, said Ris, no one is sleeping overnight at the aquarium “except 30,000 fish.’’ Both Ris and Rogers have noted that many major cities provide direct funding for their major tourist attractions, while Boston takes the opposite tack.

The Municipal Research Bureau report sympathizes with cultural institutions that struggle during fluctuations in the economy. It notes that the city’s PILOT formula already allows an institution to fulfill up to 50 percent of its obligation in the form of scholarships, summer jobs, and other community benefits. So why not allow the cultural institutions to exceed that 50 percent threshold and even, in some cases, make no cash payments at all?

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That’s a Solomonic solution from the Research Bureau. But it still rankles. The decision to pay nothing — even a reduced payment — suggests arrogance, whether coming from a museum or an educational institution. Take the case of the private Roxbury Latin School, which sits on a $52 million property in West Roxbury. It ignored the city’s request for $29,000 under the formula. This is the same Roxbury Latin School, mind you, that made off with a bronze casting of Revolutionary patriot Joseph Warren back in 1969 and has refused to return it to its rightful place on Warren Street in Roxbury ever since. How about if next year’s PILOT payment from Roxbury Latin includes cash, in-kind services, and the return of the hostage statue? Don’t hold your breath.

The PILOT controversy will intensify over the next few years as the payment schedules ramp up. Some institutions may make a good case that the city’s formula is too aggressive, inhibiting a healthy, symbiotic relationship. But those who pay nothing will risk being seen as parasites.